Pre-Algebra
Ratios and rates
Scale and scale models
20 practice questions
0 video lessons
Theory + worked examples
Scale and Scale Models
California Pre-Algebra • Standard 7.G.1 • Ratios & Rates
Scale and Scale Models is a topic in Ratios & Rates in the California Common Core State Standards. It is aligned to Standard 7.G.1, which requires students to use scale and scale factors to solve problems with maps and models.
A scale relates a drawing or model to the actual object by a constant factor, used in maps and models.
Theory
A scale is the ratio of a drawing or model size to the actual size, such as \(1\text{ in}:50\text{ mi}\).
Multiply by the scale factor to go from drawing to actual, divide to go back.
A scale factor enlarges.
Reading a scale.
Scale relationship:
\[\dfrac{\text{drawing}}{\text{actual}}=\text{scale}\]
Use the same units to find a scale factor.
How to use a scale
- Write the scale as a ratio.
- Set up a proportion with the known length.
- Solve for the unknown length.
- Match units before comparing.
Example 1 — Use a scale
A map scale is \(1\text{ in}:20\text{ mi}\). How far is \(3.5\) in?
Solution
Multiply by \(20\).
| \(3.5\cdot20\) | \(=\) | \(70\text{ mi}\) |
Example 2 — Find drawing length
At \(1:50\), a \(300\)-cm wall is how long in the drawing?
Solution
Divide by \(50\).
| \(\dfrac{300}{50}\) | \(=\) | \(6\text{ cm}\) |
Example 3 — Scale factor
A model is \(2\) in for an actual \(6\) ft. Find the scale factor.
Solution
Same units: \(6\text{ ft}=72\text{ in}\).
| \(\dfrac{2}{72}\) | \(=\) | \(\dfrac{1}{36}\) |
Example 4 — Enlarge
A photo \(4\times6\) is enlarged by \(3\). Find the new size.
Solution
Multiply each side.
| \(12\times18\) |
Common pitfalls
Match the units before finding a scale factor.
Multiply to enlarge, divide to reduce.
Scale keeps the shape, only the size changes.
Frequently asked questions
What is a scale?
The ratio of drawing size to actual size.
How do I find an actual distance?
Multiply the drawing length by the scale.
\(1\text{ in}:20\text{ mi}\), how far is \(3.5\) in?
\(70\) miles.
Does scaling change the shape?
No, only the size.
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